# Referee Response: Efficiency Regression Audit

Efficiency = log(patents_per_million / rd_expenditure_gdp)
- N with valid efficiency: 738, countries: 44

## D1: Z_1, Z_2, Z_3 → Efficiency

N = 693, Countries = 41, R² = 0.0748, ρ = 0.990

| Variable | Coef | SE | p-value | Sig |
|---|---|---|---|---|
| Z_1 | 0.0116 | 3.7541 | 0.9975 |  |
| Z_2 | 0.2403 | 0.5395 | 0.6562 |  |
| Z_3 | -0.0152 | 0.0214 | 0.4788 |  |
| rgdp_growth | 0.0051 | 0.0022 | 0.0199 | ** |
| kaopen | 0.0006 | 0.0313 | 0.9845 |  |

## D2: old_dep, youth_dep → Efficiency

N = 693, Countries = 41, R² = 0.0922, ρ = 0.985

| Variable | Coef | SE | p-value | Sig |
|---|---|---|---|---|
| old_dep | -3.4754 | 1.6068 | 0.0309 | ** |
| youth_dep | -3.2228 | 0.8819 | 0.0003 | *** |
| rgdp_growth | 0.0051 | 0.0022 | 0.0211 | ** |
| kaopen | 0.0026 | 0.0313 | 0.9327 |  |

## Interpretation
- Z_1 on efficiency: p = 0.9975 → **not significant**
- old_dep on efficiency: p = 0.0309 → **significant**

Confirmed: Z_1 is null on efficiency while old_dep is significant. The PCA components capture different variation than the raw dependency ratio.
